I've known people put the disclaimer in the beginning or the end of the issue/episode, some small note like 'this episode contains lyrics from' and yada yada. That way it doesn't break the immersion.
That includes, like, serialized and published printed work sold for money, and as far as I'm aware they didn't have to buy any rights for that, so I'd guess legally a disclaimer should be enough (doubly so if you're not monetizing it), especially since it's just a fragment and not, like, the whole body your entire work hinges on.
I have song lyrics in some upcoming episodes, but they are translated from another language by me personally, so it's technically an adaptation. So I'm just gonna credit the song in the description of the first page it appears in.